Related papers: Classifying Nichols algebras over classical Weyl g…

In this paper, we consider the Drinfeld double $\D$ of a $12$-dimensional Hopf algebra $\C$ over an algebraically closed field of characteristic zero whose coradical is not a subalgebra and describe its simple modules, projective covers of…

The orbits of Weyl groups W(B(n)), W(C(n)) and W(D(n)) of the simple Lie algebras B(n), C(n) and D(n) are reduced to the union of the orbits of Weyl groups of the maximal reductive subalgebras of B(n), C(n) and D(n). Matrices transforming…

The aim of this paper is to give relations between the category of finetely generated graded modules over the homogeneized Weyl algebra $B_{n}$, the finetely generated modules over the Weyl algebra $A_{n}$ and the finetely generated graded…

We determine the combinatorics of transitive module categories over the monoidal category of finite dimensional $\mathfrak{sl}_3$-modules which arise when acting by the latter monoidal category on arbitrary simple $\mathfrak{sl}_3$-modules.…

For any $n$ nonnegative integer a family of groups, denoted by $ \mathcal{D}_n $, was introduce by Bianchi et al., as the collection of all finite groups with exactly $n$ conjugacy classes of nontrivial, non self-normalizing subgroups. It…

We show that various invariants of a unipotent conjugacy class in a connected semisimple group can be recovered purely in terms of data involving the Weyl group.

We translate the concept of restriction of an arrangement in terms of Hopf algebras. In consequence, every Nichols algebra gives rise to a simplicial complex decorated by Nichols algebras with restricted root systems. As applications, some…

Let $A$ be a $Z$-graded associative algebra and let $\rho$ be an irreducible $N$-graded representation of $A$ on $W$ with finite-dimensional homogeneous subspaces. Then it is proved that $\rho(\tilde{A})=gl_{J}(W)$, where $\tilde{A}$ is the…

Let $n>1$ be an integer, $\alpha\in{\mathbb C}^n$, $b\in{\mathbb C}$, and $V$ a $\mathfrak{gl}_n$-module. We define a class of weight modules $F^\alpha_{b}(V)$ over $\sl_{n+1}$ using the restriction of modules of tensor fields over the Lie…

In this paper, we will compute the characteristic polynomials for finite dimensional representations of classical complex Lie algebras and the exceptional Lie algebra of type G2, which can be obtained through the orbits of integral weights…

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on…

We describe the multiplicative invariant algebras of the root lattices of all irreducible root systems under the action of the Weyl group. In each case, a finite system of fundamental invariants is determined and the class group of the…

This paper is a first step toward the full description of a family of Hopf algebras whose coradical is isomorphic to a semisimple Hopf algebra K_{n}, n an odd positive integer, obtained by a cocentral abelian cleft extension. We describe…

In this paper, we study weight representations over the Schr{\"o}dinger Lie algebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that the algebra $\mathfrak{s}_n$ can be realized by polynomial differential operators. Using…

We classify up to isomorphism all finite-dimensional Lie algebras that can be realised as Lie subalgebras of the complex Weyl algebra $A_1$. The list we obtain turns out to be discrete and for example, the only non-solvable Lie algebras…

We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…

In this article, we study the derivations of group algebras of some important groups, namely, dihedral ($D_{2n}$), Dicyclic ($T_{4n}$) and Semi-dihedral ($SD_{8n}$). First, we explicitly classify all inner derivations of a group algebra…

Motivated by the study of invariant rings of finite groups on the first Weyl algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced and studied by…

Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra $\G\otimes{\bf C}[\lambda,\lambda^{-1}]$ are studied. The graded…

In this paper, by using the "twisting technique" we obtain a class of new modules $A_b$ over the Witt algebras $\mathcal{W}_n$ from modules $A$ over the Weyl algebras $\mathcal{K}_n$ (of Laurent polynomials) for any $b\in\mathbb{C}$. We…